From geometry to generating functions: rectangulations and permutations

Abstract

We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and Mütze. We also analyze a new class of rectangulations, called whirls, using a generating tree.

To appear in the proceedings of FPSAC 2024 (to be published in the Séminaire Lotharingien de Combinatoire)